Theorem bj-nnst 13318

Description: Double negation of stability of a formula. Intuitionistic logic refutes unstability (but does not prove stability) of any formula. This theorem can also be proved in classical refutability calculus (see set.mm/bj-peircestab) but not in minimal calculus (see set.mm/bj-stabpeirce). (Contributed by BJ, 9-Oct-2019.)

Assertion

Ref	Expression
bj-nnst	|- -. -. STAB ph

Proof of Theorem bj-nnst

Step	Hyp	Ref	Expression
1		nndc 837	. 2 |- -. -. DECID ph
2		dcstab 830	. . 3 |- (DECID ph -> STAB ph )
3	2	con3i 622	. 2 |- ( -. STAB ph -> -. DECID ph )
4	1, 3	mto 652	1 |- -. -. STAB ph

Syntax hints:   -. wn 3  STAB wstab 816  DECID wdc 820

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699

This theorem depends on definitions:  df-bi 116  df-stab 817  df-dc 821

This theorem is referenced by:  bj-dcst  13321  bj-stst  13322